In this paper we characterize the Fourier transformability of a strongly almost periodic measure in terms of an integrability condition for its Fourier Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be a Fourier transform of a measure. We discuss the Fourier transformability of a measure on $\RR^d$ in terms of its Fourier transform as a tempered distribution. We conclude by looking at a large class of such measures coming from the cut and project formalism.
The aim of this work is to study the existence of a periodic solutions of integro-differential equations d dt [x(t)-- L(x t)] = A[x(t)-- L(x t)]+ G(x t)+ t --$\infty$ a(t-- s)x(s)ds+ f (t), (0 $\le$ t $\le$ 2$π$) with the periodic condition x(0) = x(2$π$), where a $\in$ L 1 (R +). Our approach is based on the M-boundedness of linear operators, Fourier type, B s p,q-multipliers and Besov spaces.
本文研究了当$1 \leq d \leq n-1$满足一定条件时，未知函数在平坦$n$环面上的$d$平面Radon变换的重构问题.我们证明了新的重建公式和稳定性结果加权贝塞尔潜在的规范。利用伴随算子和正规算子的性质，解决了$H^s$索伯列夫空间上的Tikhonov极小化问题.其中一个反演公式表明，平面上一个平均为零的紧支分布是其X射线数据的加权和。
